The method of fundamental solutions for eigenfrequencies of plate vibrations

Abstract

This paper describes the method of fundamental solutions (MFS) to solve eigenfrequencies ofplate vibrations by utilizing the direct determinant searchmethod. The complex-valued kernels are used in theMFS in order to avoid the spurious eigenvalues. Thebenchmark problems of a circular plate with clamped,simply supported and free boundary conditions are studied analytically as well as numerically using the discreteand continuous versions of the MFS schemes to demonstrate the major results of the present paper. Namely onlytrue eigenvalues are contained and no spurious eigenvalues are included in the range of direct determinant searchmethod. Consequently analytical derivation is carried outby using the degenerate kernels and Fourier series to obtain the exact eigenvalues which are used to validate thenumerical methods. The MFS is free from meshes, singularities, and numerical integrations. As a result, theproposed numerical method can be easily used to solveplate vibrations free from spurious eigenvalues in simplyconnected domains.